A016629 - OEIS

A016629

Decimal expansion of log(6).

1, 7, 9, 1, 7, 5, 9, 4, 6, 9, 2, 2, 8, 0, 5, 5, 0, 0, 0, 8, 1, 2, 4, 7, 7, 3, 5, 8, 3, 8, 0, 7, 0, 2, 2, 7, 2, 7, 2, 2, 9, 9, 0, 6, 9, 2, 1, 8, 3, 0, 0, 4, 7, 0, 5, 8, 5, 5, 3, 7, 4, 3, 4, 3, 1, 3, 0, 8, 8, 7, 9, 1, 5, 1, 8, 8, 3, 0, 3, 6, 8, 2, 4, 7, 9, 4, 7, 9, 0, 8, 1, 8, 1, 0, 1, 5, 0, 7, 7

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Matt Parker, What's the story with log(1 + 2 + 3)?, standupmaths video (2019)

Index entries for transcendental numbers

FORMULA

log(6) = 2*Sum_{n >= 1} 1/(n*P(n, 7/5)*P(n-1, 7/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(6) = 1.79175946922805(27...), correct to 14 decimal places. - Peter Bala, Mar 19 2024

Equals A002162 + A002391. - R. J. Mathar, Jun 10 2024

EXAMPLE

1.791759469228055000812477358380702272722990692183004705855374343130887...

MATHEMATICA

First[RealDigits[Log[6], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)

PROG

(PARI) default(realprecision, 20080); x=log(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016629.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009

CROSSREFS

Cf. A016734 (continued fraction).

Sequence in context: A244674 A130834 A132806 * A154203 A375189 A055676

Adjacent sequences: A016626 A016627 A016628 * A016630 A016631 A016632

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved